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lbfgs.c
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lbfgs.c
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/*
* Limited memory BFGS (L-BFGS).
*
* Copyright (c) 1990, Jorge Nocedal
* Copyright (c) 2007-2010 Naoaki Okazaki
* All rights reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
/* $Id$ */
/*
This library is a C port of the FORTRAN implementation of Limited-memory
Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method written by Jorge Nocedal.
The original FORTRAN source code is available at:
http://www.ece.northwestern.edu/~nocedal/lbfgs.html
The L-BFGS algorithm is described in:
- Jorge Nocedal.
Updating Quasi-Newton Matrices with Limited Storage.
<i>Mathematics of Computation</i>, Vol. 35, No. 151, pp. 773--782, 1980.
- Dong C. Liu and Jorge Nocedal.
On the limited memory BFGS method for large scale optimization.
<i>Mathematical Programming</i> B, Vol. 45, No. 3, pp. 503-528, 1989.
The line search algorithms used in this implementation are described in:
- John E. Dennis and Robert B. Schnabel.
<i>Numerical Methods for Unconstrained Optimization and Nonlinear
Equations</i>, Englewood Cliffs, 1983.
- Jorge J. More and David J. Thuente.
Line search algorithm with guaranteed sufficient decrease.
<i>ACM Transactions on Mathematical Software (TOMS)</i>, Vol. 20, No. 3,
pp. 286-307, 1994.
This library also implements Orthant-Wise Limited-memory Quasi-Newton (OWL-QN)
method presented in:
- Galen Andrew and Jianfeng Gao.
Scalable training of L1-regularized log-linear models.
In <i>Proceedings of the 24th International Conference on Machine
Learning (ICML 2007)</i>, pp. 33-40, 2007.
I would like to thank the original author, Jorge Nocedal, who has been
distributing the effieicnt and explanatory implementation in an open source
licence.
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif/*HAVE_CONFIG_H*/
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "lbfgs.h"
#ifdef _MSC_VER
#define inline __inline
#endif/*_MSC_VER*/
#if defined(USE_SSE) && defined(__SSE2__) && LBFGS_FLOAT == 64
/* Use SSE2 optimization for 64bit double precision. */
#include "arithmetic_sse_double.h"
#elif defined(USE_SSE) && defined(__SSE__) && LBFGS_FLOAT == 32
/* Use SSE optimization for 32bit float precision. */
#include "arithmetic_sse_float.h"
#else
/* No CPU specific optimization. */
#include "arithmetic_ansi.h"
#endif
#define min2(a, b) ((a) <= (b) ? (a) : (b))
#define max2(a, b) ((a) >= (b) ? (a) : (b))
#define max3(a, b, c) max2(max2((a), (b)), (c));
struct tag_callback_data {
int n;
void *instance;
lbfgs_evaluate_t proc_evaluate;
lbfgs_progress_t proc_progress;
};
typedef struct tag_callback_data callback_data_t;
struct tag_iteration_data {
lbfgsfloatval_t alpha;
lbfgsfloatval_t *s; /* [n] */
lbfgsfloatval_t *y; /* [n] */
lbfgsfloatval_t ys; /* vecdot(y, s) */
};
typedef struct tag_iteration_data iteration_data_t;
static const lbfgs_parameter_t _defparam = {
6, 1e-5, 0, 1e-5,
0, LBFGS_LINESEARCH_DEFAULT, 40,
1e-20, 1e20, 1e-4, 0.9, 0.9, 1.0e-16,
0.0, 0, -1,
};
/* Forward function declarations. */
typedef int (*line_search_proc)(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wa,
callback_data_t *cd,
const lbfgs_parameter_t *param
);
static int line_search_backtracking(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wa,
callback_data_t *cd,
const lbfgs_parameter_t *param
);
static int line_search_backtracking_owlqn(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wp,
callback_data_t *cd,
const lbfgs_parameter_t *param
);
static int line_search_morethuente(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wa,
callback_data_t *cd,
const lbfgs_parameter_t *param
);
static int update_trial_interval(
lbfgsfloatval_t *x,
lbfgsfloatval_t *fx,
lbfgsfloatval_t *dx,
lbfgsfloatval_t *y,
lbfgsfloatval_t *fy,
lbfgsfloatval_t *dy,
lbfgsfloatval_t *t,
lbfgsfloatval_t *ft,
lbfgsfloatval_t *dt,
const lbfgsfloatval_t tmin,
const lbfgsfloatval_t tmax,
int *brackt
);
static lbfgsfloatval_t owlqn_x1norm(
const lbfgsfloatval_t* x,
const int start,
const int n
);
static void owlqn_pseudo_gradient(
lbfgsfloatval_t* pg,
const lbfgsfloatval_t* x,
const lbfgsfloatval_t* g,
const int n,
const lbfgsfloatval_t c,
const int start,
const int end
);
static void owlqn_project(
lbfgsfloatval_t* d,
const lbfgsfloatval_t* sign,
const int start,
const int end
);
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
static int round_out_variables(int n)
{
n += 7;
n /= 8;
n *= 8;
return n;
}
#endif/*defined(USE_SSE)*/
lbfgsfloatval_t* lbfgs_malloc(int n)
{
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
n = round_out_variables(n);
#endif/*defined(USE_SSE)*/
return (lbfgsfloatval_t*)vecalloc(sizeof(lbfgsfloatval_t) * n);
}
void lbfgs_free(lbfgsfloatval_t *x)
{
vecfree(x);
}
void lbfgs_parameter_init(lbfgs_parameter_t *param)
{
memcpy(param, &_defparam, sizeof(*param));
}
int lbfgs(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *ptr_fx,
lbfgs_evaluate_t proc_evaluate,
lbfgs_progress_t proc_progress,
void *instance,
lbfgs_parameter_t *_param
)
{
int ret;
int i, j, k, ls, end, bound;
lbfgsfloatval_t step;
/* Constant parameters and their default values. */
lbfgs_parameter_t param = (_param != NULL) ? (*_param) : _defparam;
const int m = param.m;
lbfgsfloatval_t *xp = NULL;
lbfgsfloatval_t *g = NULL, *gp = NULL, *pg = NULL;
lbfgsfloatval_t *d = NULL, *w = NULL, *pf = NULL;
iteration_data_t *lm = NULL, *it = NULL;
lbfgsfloatval_t ys, yy;
lbfgsfloatval_t xnorm, gnorm, beta;
lbfgsfloatval_t fx = 0.;
lbfgsfloatval_t rate = 0.;
line_search_proc linesearch = line_search_morethuente;
/* Construct a callback data. */
callback_data_t cd;
cd.n = n;
cd.instance = instance;
cd.proc_evaluate = proc_evaluate;
cd.proc_progress = proc_progress;
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
/* Round out the number of variables. */
n = round_out_variables(n);
#endif/*defined(USE_SSE)*/
/* Check the input parameters for errors. */
if (n <= 0) {
return LBFGSERR_INVALID_N;
}
#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))
if (n % 8 != 0) {
return LBFGSERR_INVALID_N_SSE;
}
if ((uintptr_t)(const void*)x % 16 != 0) {
return LBFGSERR_INVALID_X_SSE;
}
#endif/*defined(USE_SSE)*/
if (param.epsilon < 0.) {
return LBFGSERR_INVALID_EPSILON;
}
if (param.past < 0) {
return LBFGSERR_INVALID_TESTPERIOD;
}
if (param.delta < 0.) {
return LBFGSERR_INVALID_DELTA;
}
if (param.min_step < 0.) {
return LBFGSERR_INVALID_MINSTEP;
}
if (param.max_step < param.min_step) {
return LBFGSERR_INVALID_MAXSTEP;
}
if (param.ftol < 0.) {
return LBFGSERR_INVALID_FTOL;
}
if (param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE ||
param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE) {
if (param.wolfe <= param.ftol || 1. <= param.wolfe) {
return LBFGSERR_INVALID_WOLFE;
}
}
if (param.gtol < 0.) {
return LBFGSERR_INVALID_GTOL;
}
if (param.xtol < 0.) {
return LBFGSERR_INVALID_XTOL;
}
if (param.max_linesearch <= 0) {
return LBFGSERR_INVALID_MAXLINESEARCH;
}
if (param.orthantwise_c < 0.) {
return LBFGSERR_INVALID_ORTHANTWISE;
}
if (param.orthantwise_start < 0 || n < param.orthantwise_start) {
return LBFGSERR_INVALID_ORTHANTWISE_START;
}
if (param.orthantwise_end < 0) {
param.orthantwise_end = n;
}
if (n < param.orthantwise_end) {
return LBFGSERR_INVALID_ORTHANTWISE_END;
}
if (param.orthantwise_c != 0.) {
switch (param.linesearch) {
case LBFGS_LINESEARCH_BACKTRACKING:
linesearch = line_search_backtracking_owlqn;
break;
default:
/* Only the backtracking method is available. */
return LBFGSERR_INVALID_LINESEARCH;
}
} else {
switch (param.linesearch) {
case LBFGS_LINESEARCH_MORETHUENTE:
linesearch = line_search_morethuente;
break;
case LBFGS_LINESEARCH_BACKTRACKING_ARMIJO:
case LBFGS_LINESEARCH_BACKTRACKING_WOLFE:
case LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE:
linesearch = line_search_backtracking;
break;
default:
return LBFGSERR_INVALID_LINESEARCH;
}
}
/* Allocate working space. */
xp = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
g = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
gp = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
d = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
w = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
if (xp == NULL || g == NULL || gp == NULL || d == NULL || w == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
if (param.orthantwise_c != 0.) {
/* Allocate working space for OW-LQN. */
pg = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
if (pg == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
}
/* Allocate limited memory storage. */
lm = (iteration_data_t*)vecalloc(m * sizeof(iteration_data_t));
if (lm == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
/* Initialize the limited memory. */
for (i = 0;i < m;++i) {
it = &lm[i];
it->alpha = 0;
it->ys = 0;
it->s = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
it->y = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));
if (it->s == NULL || it->y == NULL) {
ret = LBFGSERR_OUTOFMEMORY;
goto lbfgs_exit;
}
}
/* Allocate an array for storing previous values of the objective function. */
if (0 < param.past) {
pf = (lbfgsfloatval_t*)vecalloc(param.past * sizeof(lbfgsfloatval_t));
}
/* Evaluate the function value and its gradient. */
fx = cd.proc_evaluate(cd.instance, x, g, cd.n, 0);
if (0. != param.orthantwise_c) {
/* Compute the L1 norm of the variable and add it to the object value. */
xnorm = owlqn_x1norm(x, param.orthantwise_start, param.orthantwise_end);
fx += xnorm * param.orthantwise_c;
owlqn_pseudo_gradient(
pg, x, g, n,
param.orthantwise_c, param.orthantwise_start, param.orthantwise_end
);
}
/* Store the initial value of the objective function. */
if (pf != NULL) {
pf[0] = fx;
}
/*
Compute the direction;
we assume the initial hessian matrix H_0 as the identity matrix.
*/
if (param.orthantwise_c == 0.) {
vecncpy(d, g, n);
} else {
vecncpy(d, pg, n);
}
/*
Make sure that the initial variables are not a minimizer.
*/
vec2norm(&xnorm, x, n);
if (param.orthantwise_c == 0.) {
vec2norm(&gnorm, g, n);
} else {
vec2norm(&gnorm, pg, n);
}
if (xnorm < 1.0) xnorm = 1.0;
if (gnorm / xnorm <= param.epsilon) {
ret = LBFGS_ALREADY_MINIMIZED;
goto lbfgs_exit;
}
/* Compute the initial step:
step = 1.0 / sqrt(vecdot(d, d, n))
*/
vec2norminv(&step, d, n);
k = 1;
end = 0;
for (;;) {
/* Store the current position and gradient vectors. */
veccpy(xp, x, n);
veccpy(gp, g, n);
/* Search for an optimal step. */
if (param.orthantwise_c == 0.) {
ls = linesearch(n, x, &fx, g, d, &step, xp, gp, w, &cd, ¶m);
} else {
ls = linesearch(n, x, &fx, g, d, &step, xp, pg, w, &cd, ¶m);
owlqn_pseudo_gradient(
pg, x, g, n,
param.orthantwise_c, param.orthantwise_start, param.orthantwise_end
);
}
if (ls < 0) {
/* Revert to the previous point. */
veccpy(x, xp, n);
veccpy(g, gp, n);
ret = ls;
goto lbfgs_exit;
}
/* Compute x and g norms. */
vec2norm(&xnorm, x, n);
if (param.orthantwise_c == 0.) {
vec2norm(&gnorm, g, n);
} else {
vec2norm(&gnorm, pg, n);
}
/* Report the progress. */
if (cd.proc_progress) {
if ((ret = cd.proc_progress(cd.instance, x, g, fx, xnorm, gnorm, step, cd.n, k, ls))) {
goto lbfgs_exit;
}
}
/*
Convergence test.
The criterion is given by the following formula:
|g(x)| / \max(1, |x|) < \epsilon
*/
if (xnorm < 1.0) xnorm = 1.0;
if (gnorm / xnorm <= param.epsilon) {
/* Convergence. */
ret = LBFGS_SUCCESS;
break;
}
/*
Test for stopping criterion.
The criterion is given by the following formula:
(f(past_x) - f(x)) / f(x) < \delta
*/
if (pf != NULL) {
/* We don't test the stopping criterion while k < past. */
if (param.past <= k) {
/* Compute the relative improvement from the past. */
rate = (pf[k % param.past] - fx) / fx;
/* The stopping criterion. */
if (rate < param.delta) {
ret = LBFGS_STOP;
break;
}
}
/* Store the current value of the objective function. */
pf[k % param.past] = fx;
}
if (param.max_iterations != 0 && param.max_iterations < k+1) {
/* Maximum number of iterations. */
ret = LBFGSERR_MAXIMUMITERATION;
break;
}
/*
Update vectors s and y:
s_{k+1} = x_{k+1} - x_{k} = \step * d_{k}.
y_{k+1} = g_{k+1} - g_{k}.
*/
it = &lm[end];
vecdiff(it->s, x, xp, n);
vecdiff(it->y, g, gp, n);
/*
Compute scalars ys and yy:
ys = y^t \cdot s = 1 / \rho.
yy = y^t \cdot y.
Notice that yy is used for scaling the hessian matrix H_0 (Cholesky factor).
*/
vecdot(&ys, it->y, it->s, n);
vecdot(&yy, it->y, it->y, n);
it->ys = ys;
/*
Recursive formula to compute dir = -(H \cdot g).
This is described in page 779 of:
Jorge Nocedal.
Updating Quasi-Newton Matrices with Limited Storage.
Mathematics of Computation, Vol. 35, No. 151,
pp. 773--782, 1980.
*/
bound = (m <= k) ? m : k;
++k;
end = (end + 1) % m;
/* Compute the steepest direction. */
if (param.orthantwise_c == 0.) {
/* Compute the negative of gradients. */
vecncpy(d, g, n);
} else {
vecncpy(d, pg, n);
}
j = end;
for (i = 0;i < bound;++i) {
j = (j + m - 1) % m; /* if (--j == -1) j = m-1; */
it = &lm[j];
/* \alpha_{j} = \rho_{j} s^{t}_{j} \cdot q_{k+1}. */
vecdot(&it->alpha, it->s, d, n);
it->alpha /= it->ys;
/* q_{i} = q_{i+1} - \alpha_{i} y_{i}. */
vecadd(d, it->y, -it->alpha, n);
}
vecscale(d, ys / yy, n);
for (i = 0;i < bound;++i) {
it = &lm[j];
/* \beta_{j} = \rho_{j} y^t_{j} \cdot \gamma_{i}. */
vecdot(&beta, it->y, d, n);
beta /= it->ys;
/* \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j}. */
vecadd(d, it->s, it->alpha - beta, n);
j = (j + 1) % m; /* if (++j == m) j = 0; */
}
/*
Constrain the search direction for orthant-wise updates.
*/
if (param.orthantwise_c != 0.) {
for (i = param.orthantwise_start;i < param.orthantwise_end;++i) {
if (d[i] * pg[i] >= 0) {
d[i] = 0;
}
}
}
/*
Now the search direction d is ready. We try step = 1 first.
*/
step = 1.0;
}
lbfgs_exit:
/* Return the final value of the objective function. */
if (ptr_fx != NULL) {
*ptr_fx = fx;
}
vecfree(pf);
/* Free memory blocks used by this function. */
if (lm != NULL) {
for (i = 0;i < m;++i) {
vecfree(lm[i].s);
vecfree(lm[i].y);
}
vecfree(lm);
}
vecfree(pg);
vecfree(w);
vecfree(d);
vecfree(gp);
vecfree(g);
vecfree(xp);
return ret;
}
static int line_search_backtracking(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wp,
callback_data_t *cd,
const lbfgs_parameter_t *param
)
{
int count = 0;
lbfgsfloatval_t width, dg;
lbfgsfloatval_t finit, dginit = 0., dgtest;
const lbfgsfloatval_t dec = 0.5, inc = 2.1;
/* Check the input parameters for errors. */
if (*stp <= 0.) {
return LBFGSERR_INVALIDPARAMETERS;
}
/* Compute the initial gradient in the search direction. */
vecdot(&dginit, g, s, n);
/* Make sure that s points to a descent direction. */
if (0 < dginit) {
return LBFGSERR_INCREASEGRADIENT;
}
/* The initial value of the objective function. */
finit = *f;
dgtest = param->ftol * dginit;
for (;;) {
veccpy(x, xp, n);
vecadd(x, s, *stp, n);
/* Evaluate the function and gradient values. */
*f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);
++count;
if (*f > finit + *stp * dgtest) {
width = dec;
} else {
/* The sufficient decrease condition (Armijo condition). */
if (param->linesearch == LBFGS_LINESEARCH_BACKTRACKING_ARMIJO) {
/* Exit with the Armijo condition. */
return count;
}
/* Check the Wolfe condition. */
vecdot(&dg, g, s, n);
if (dg < param->wolfe * dginit) {
width = inc;
} else {
if(param->linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE) {
/* Exit with the regular Wolfe condition. */
return count;
}
/* Check the strong Wolfe condition. */
if(dg > -param->wolfe * dginit) {
width = dec;
} else {
/* Exit with the strong Wolfe condition. */
return count;
}
}
}
if (*stp < param->min_step) {
/* The step is the minimum value. */
return LBFGSERR_MINIMUMSTEP;
}
if (*stp > param->max_step) {
/* The step is the maximum value. */
return LBFGSERR_MAXIMUMSTEP;
}
if (param->max_linesearch <= count) {
/* Maximum number of iteration. */
return LBFGSERR_MAXIMUMLINESEARCH;
}
(*stp) *= width;
}
}
static int line_search_backtracking_owlqn(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wp,
callback_data_t *cd,
const lbfgs_parameter_t *param
)
{
int i, count = 0;
lbfgsfloatval_t width = 0.5, norm = 0.;
lbfgsfloatval_t finit = *f, dgtest;
/* Check the input parameters for errors. */
if (*stp <= 0.) {
return LBFGSERR_INVALIDPARAMETERS;
}
/* Choose the orthant for the new point. */
for (i = 0;i < n;++i) {
wp[i] = (xp[i] == 0.) ? -gp[i] : xp[i];
}
for (;;) {
/* Update the current point. */
veccpy(x, xp, n);
vecadd(x, s, *stp, n);
/* The current point is projected onto the orthant. */
owlqn_project(x, wp, param->orthantwise_start, param->orthantwise_end);
/* Evaluate the function and gradient values. */
*f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);
/* Compute the L1 norm of the variables and add it to the object value. */
norm = owlqn_x1norm(x, param->orthantwise_start, param->orthantwise_end);
*f += norm * param->orthantwise_c;
++count;
dgtest = 0.;
for (i = 0;i < n;++i) {
dgtest += (x[i] - xp[i]) * gp[i];
}
if (*f <= finit + param->ftol * dgtest) {
/* The sufficient decrease condition. */
return count;
}
if (*stp < param->min_step) {
/* The step is the minimum value. */
return LBFGSERR_MINIMUMSTEP;
}
if (*stp > param->max_step) {
/* The step is the maximum value. */
return LBFGSERR_MAXIMUMSTEP;
}
if (param->max_linesearch <= count) {
/* Maximum number of iteration. */
return LBFGSERR_MAXIMUMLINESEARCH;
}
(*stp) *= width;
}
}
static int line_search_morethuente(
int n,
lbfgsfloatval_t *x,
lbfgsfloatval_t *f,
lbfgsfloatval_t *g,
lbfgsfloatval_t *s,
lbfgsfloatval_t *stp,
const lbfgsfloatval_t* xp,
const lbfgsfloatval_t* gp,
lbfgsfloatval_t *wa,
callback_data_t *cd,
const lbfgs_parameter_t *param
)
{
int count = 0;
int brackt, stage1, uinfo = 0;
lbfgsfloatval_t dg;
lbfgsfloatval_t stx, fx, dgx;
lbfgsfloatval_t sty, fy, dgy;
lbfgsfloatval_t fxm, dgxm, fym, dgym, fm, dgm;
lbfgsfloatval_t finit, ftest1, dginit, dgtest;
lbfgsfloatval_t width, prev_width;
lbfgsfloatval_t stmin, stmax;
/* Check the input parameters for errors. */
if (*stp <= 0.) {
return LBFGSERR_INVALIDPARAMETERS;
}
/* Compute the initial gradient in the search direction. */
vecdot(&dginit, g, s, n);
/* Make sure that s points to a descent direction. */
if (0 < dginit) {
return LBFGSERR_INCREASEGRADIENT;
}
/* Initialize local variables. */
brackt = 0;
stage1 = 1;
finit = *f;
dgtest = param->ftol * dginit;
width = param->max_step - param->min_step;
prev_width = 2.0 * width;
/*
The variables stx, fx, dgx contain the values of the step,
function, and directional derivative at the best step.
The variables sty, fy, dgy contain the value of the step,
function, and derivative at the other endpoint of
the interval of uncertainty.
The variables stp, f, dg contain the values of the step,
function, and derivative at the current step.
*/
stx = sty = 0.;
fx = fy = finit;
dgx = dgy = dginit;
for (;;) {
/*
Set the minimum and maximum steps to correspond to the
present interval of uncertainty.
*/
if (brackt) {
stmin = min2(stx, sty);
stmax = max2(stx, sty);
} else {
stmin = stx;
stmax = *stp + 4.0 * (*stp - stx);
}
/* Clip the step in the range of [stpmin, stpmax]. */
if (*stp < param->min_step) *stp = param->min_step;
if (param->max_step < *stp) *stp = param->max_step;
/*
If an unusual termination is to occur then let
stp be the lowest point obtained so far.
*/
if ((brackt && ((*stp <= stmin || stmax <= *stp) || param->max_linesearch <= count + 1 || uinfo != 0)) || (brackt && (stmax - stmin <= param->xtol * stmax))) {
*stp = stx;
}
/*
Compute the current value of x:
x <- x + (*stp) * s.
*/
veccpy(x, xp, n);
vecadd(x, s, *stp, n);
/* Evaluate the function and gradient values. */
*f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);
vecdot(&dg, g, s, n);
ftest1 = finit + *stp * dgtest;
++count;
/* Test for errors and convergence. */
if (brackt && ((*stp <= stmin || stmax <= *stp) || uinfo != 0)) {
/* Rounding errors prevent further progress. */
return LBFGSERR_ROUNDING_ERROR;
}
if (*stp == param->max_step && *f <= ftest1 && dg <= dgtest) {
/* The step is the maximum value. */
return LBFGSERR_MAXIMUMSTEP;
}
if (*stp == param->min_step && (ftest1 < *f || dgtest <= dg)) {
/* The step is the minimum value. */
return LBFGSERR_MINIMUMSTEP;
}
if (brackt && (stmax - stmin) <= param->xtol * stmax) {
/* Relative width of the interval of uncertainty is at most xtol. */
return LBFGSERR_WIDTHTOOSMALL;
}
if (param->max_linesearch <= count) {
/* Maximum number of iteration. */
return LBFGSERR_MAXIMUMLINESEARCH;
}
if (*f <= ftest1 && fabs(dg) <= param->gtol * (-dginit)) {
/* The sufficient decrease condition and the directional derivative condition hold. */
return count;
}
/*
In the first stage we seek a step for which the modified
function has a nonpositive value and nonnegative derivative.
*/
if (stage1 && *f <= ftest1 && min2(param->ftol, param->gtol) * dginit <= dg) {
stage1 = 0;
}
/*
A modified function is used to predict the step only if
we have not obtained a step for which the modified
function has a nonpositive function value and nonnegative
derivative, and if a lower function value has been
obtained but the decrease is not sufficient.
*/
if (stage1 && ftest1 < *f && *f <= fx) {
/* Define the modified function and derivative values. */
fm = *f - *stp * dgtest;
fxm = fx - stx * dgtest;
fym = fy - sty * dgtest;
dgm = dg - dgtest;
dgxm = dgx - dgtest;
dgym = dgy - dgtest;
/*
Call update_trial_interval() to update the interval of
uncertainty and to compute the new step.
*/
uinfo = update_trial_interval(
&stx, &fxm, &dgxm,
&sty, &fym, &dgym,
stp, &fm, &dgm,
stmin, stmax, &brackt
);
/* Reset the function and gradient values for f. */
fx = fxm + stx * dgtest;
fy = fym + sty * dgtest;
dgx = dgxm + dgtest;
dgy = dgym + dgtest;
} else {
/*
Call update_trial_interval() to update the interval of
uncertainty and to compute the new step.
*/
uinfo = update_trial_interval(
&stx, &fx, &dgx,
&sty, &fy, &dgy,
stp, f, &dg,
stmin, stmax, &brackt
);
}
/*
Force a sufficient decrease in the interval of uncertainty.
*/
if (brackt) {
if (0.66 * prev_width <= fabs(sty - stx)) {
*stp = stx + 0.5 * (sty - stx);
}
prev_width = width;
width = fabs(sty - stx);
}
}
return LBFGSERR_LOGICERROR;